Zustandsklassifikation von nichtlinearen dynamischen Systemen mit Zellularen Neuronalen Netzen und mit Untersuchung des Phasenskalierungsverhaltens

Abstract

During the last years different methods from non-linear time series analysis have been successfully applied to classify the dynamics of complex systems in a number of disciplines, including physics, astrophysics, biology, chemistry, and the neurosciences. One of the most challenging complex systems is the brain. Here, pathological alterations like epilepsy introduce non-linear deterministic structures in an otherwise linear stochastic background activity. In the present study the dynamics of the epileptic brain was examined by using a Cellular Neural Network (CNN) and by determining the scaling properties of a phase variable. The aim was a classification of the spatio-temporal dynamics and, in particular, to discriminate in time between inter-seizure and pre-seizure states as well as in space between the epileptic focal and non-focal hemisphere. Time series of brain electrical activity (EEG) with different temporal dynamics but with a similar visual appearance could be distinguished using a CNN without reducing the information content of these time series. A spatial classification was based on the scaling properties of a phase variable estimated for band-pass filtered multi-channel EEG recordings in order to examine scale invariance and persistence. A characteristic scaling behaviour of the phase, with persistence in all classical EEG frequency bands, could be observed which allowed to distinguish the focal from the non-focal hemisphere in all investigated patients. The time series analysis techniques investigated here might provide further insights into the spatio-temporal dynamics of complex systems other than the epileptic brain.